Theorems · Theorem · combinatorics
Multiset.sum_bind
∀ {α : Type u_1} {β : Type v} [inst : AddCommMonoid β] (s : Multiset α) (t : α → Multiset β),
(s.bind t).sum = (Multiset.map (fun a => (t a).sum) s).sum- Defined in
- Mathlib.Data.Multiset.Bind
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Multisetstatement and proof · cited by 2,627
- Multiset.mapstatement and proof · cited by 876
- Multiset.sumstatement and proof · cited by 388
- Multiset.map_congrproof · cited by 232
- Multiset.map_mapproof · cited by 151
- Multiset.bindstatement · cited by 59
- Multiset.sum_joinproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Multiset.prod_X_add_C_eq_sum_esymmproof · cited by 3
- Multiset.prod_map_sumproof · cited by 0